Multivariate analysis by data depth: descriptive statistics, graphics and inference, (with discussion and a rejoinder by Liu and Singh)
Multivariate analysis by data depth: descriptive statistics, graphics and inference, (with discussion and a rejoinder by Liu and Singh)
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DOI：
10.1214/aos/1018031260
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发表时间：
1999-06
影响因子：
4.5
通讯作者：
Regina Y. Liu;J. Parelius;Kesar Singh
中科院分区：
文献类型：
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作者：
Regina Y. Liu;J. Parelius;Kesar Singh
数据深度可以用来衡量给定的多变量样本相对于其潜在分布的“深度”或“外延”。这导致采样点的自然中心向外排序。在此基础上，介绍了用于分析位置、规模、偏差、偏度和峰度等多变量分布特征的定量方法和图解方法，以及用于比较推理方法的方法。所有的图形都是平面上的一维曲线，可以很容易地可视化和解释。“太阳爆发图”(Ž)是盒子图的二元推广。DDDepth与.深度图作为图形化的推理工具被提出和检验。介绍了检验多元正态分布的一些新的诊断工具。其中一个监测最大偏离平均值的确切增长率，而另一个监测总体离散度与特定中心区域离散度的比率。数据深度的仿射不变性也导致了所提出的统计和方法具有适当的不变性。
A data depth can be used to measure the ‘‘depth’’ or ‘‘outlyingness’’ of a given multivariate sample with respect to its underlying distribution. This leads to a natural center-outward ordering of the sample points. Based on this ordering, quantitative and graphical methods are introduced for analyzing multivariate distributional characteristics such as location, scale, bias, skewness and kurtosis, as well as for comparing inference methods. All graphs are one-dimensional curves in the plane and can be easily visualized and interpreted. A ‘‘sunburst plot’’ is preŽ sented as a bivariate generalization of the box-plot. DDdepth versus . depth plots are proposed and examined as graphical inference tools. Some new diagnostic tools for checking multivariate normality are introduced. One of them monitors the exact rate of growth of the maximum deviation from the mean, while the others examine the ratio of the overall dispersion to the dispersion of a certain central region. The affine invariance property of a data depth also leads to appropriate invariance properties for the proposed statistics and methods.